The newspaper alleged that the on-loan from Monaco striker made a Nazi salute during Spurs' recent match against his former club Chelsea at White Hart Lane.
"I have read with horror the article in the Daily Star this morning that accuses me of making a Nazi salute," a Gudjohnsen statement reads on the club's official website
"I have this morning instructed my lawyers to take action against the paper.
"The picture shows me pointing with my first finger with my other finger over my lip. It is not and was not a Nazi salute. The suggestion that it was is an outrageous slur and I am furious that despite the paper having been clearly informed last night of the truth of the situation they nevertheless went on the publish the allegation.
"I do not see anything to do with Nazi Germany as a laughing matter and would not and have never made light of that regime.
"I am astonished that a national newspaper can so casually make such an accusation without the picture itself even backing up the allegation in what is a clear attempt to cause me immense reputational damage both personally and professionally.
"I will do all that is necessary to put that right."